Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Chapter 39, Problem 22P
To determine
The proof that most probable distance
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(a) Determine the wavelength of the second Balmerline (n=4 to n=2 transition) using Fig. 27–29. Determine likewise (b) the wavelength of the second Lyman line and (c) the wavelength of the third Balmer line.
(a) Show that the speed of an electron in the nth Bohr orbit of hydrogen is αc/n, where α is the fine structure constant, equal to e2/4πε0ħc. (b) What would be the speed in a hydrogen like atom with a nuclear charge of Ze?
.55 The radial probability density for the ground state of the
hydrogen atom is a maximum whenr = a, where a is the Bohr ra-
dius. Show that the average value of r, defined as
P(r) r dr,
has the value 1.5a. In this expression for ravgs each value of P(r) is
weighted with the value of r at which it occurs. Note that the average
value of r is greater than the value of r for which P(r) is a maximum.
Chapter 39 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 39.2 - Prob. 1AECh. 39.2 - Prob. 1BECh. 39.3 - Prob. 1CECh. 39.4 - Prob. 1DECh. 39.4 - Prob. 1EECh. 39.5 - Prob. 1FECh. 39.7 - Prob. 1GECh. 39 - Prob. 1QCh. 39 - Prob. 2QCh. 39 - Prob. 3Q
Ch. 39 - Prob. 4QCh. 39 - Prob. 5QCh. 39 - Prob. 6QCh. 39 - Prob. 7QCh. 39 - Prob. 8QCh. 39 - Prob. 9QCh. 39 - Prob. 10QCh. 39 - Prob. 11QCh. 39 - On what factors does the periodicity of the...Ch. 39 - Prob. 13QCh. 39 - Prob. 14QCh. 39 - Prob. 15QCh. 39 - Prob. 16QCh. 39 - Prob. 17QCh. 39 - Prob. 18QCh. 39 - Prob. 19QCh. 39 - Prob. 20QCh. 39 - Prob. 21QCh. 39 - Prob. 22QCh. 39 - Prob. 23QCh. 39 - Prob. 24QCh. 39 - Prob. 25QCh. 39 - Prob. 26QCh. 39 - Prob. 27QCh. 39 - Prob. 28QCh. 39 - Prob. 29QCh. 39 - Prob. 1PCh. 39 - Prob. 2PCh. 39 - Prob. 3PCh. 39 - Prob. 4PCh. 39 - Prob. 5PCh. 39 - Prob. 6PCh. 39 - Prob. 7PCh. 39 - Prob. 8PCh. 39 - Prob. 9PCh. 39 - Prob. 10PCh. 39 - Prob. 11PCh. 39 - Prob. 12PCh. 39 - Prob. 13PCh. 39 - Prob. 14PCh. 39 - Prob. 15PCh. 39 - Prob. 16PCh. 39 - Prob. 17PCh. 39 - Prob. 18PCh. 39 - Prob. 19PCh. 39 - Prob. 20PCh. 39 - Prob. 21PCh. 39 - Prob. 22PCh. 39 - Prob. 23PCh. 39 - Prob. 24PCh. 39 - Prob. 25PCh. 39 - Prob. 26PCh. 39 - Prob. 27PCh. 39 - Prob. 28PCh. 39 - Prob. 29PCh. 39 - Prob. 30PCh. 39 - Prob. 31PCh. 39 - Prob. 32PCh. 39 - Prob. 33PCh. 39 - Prob. 34PCh. 39 - Prob. 35PCh. 39 - Prob. 36PCh. 39 - Prob. 37PCh. 39 - Prob. 38PCh. 39 - Prob. 39PCh. 39 - Prob. 40PCh. 39 - Prob. 41PCh. 39 - Prob. 42PCh. 39 - Prob. 43PCh. 39 - Prob. 44PCh. 39 - Prob. 45PCh. 39 - Prob. 46PCh. 39 - Prob. 47PCh. 39 - Prob. 48PCh. 39 - Prob. 49PCh. 39 - Prob. 50PCh. 39 - Prob. 51PCh. 39 - Prob. 52PCh. 39 - Prob. 53PCh. 39 - Prob. 54PCh. 39 - Prob. 55PCh. 39 - Prob. 56PCh. 39 - Prob. 57PCh. 39 - Prob. 58PCh. 39 - Prob. 59PCh. 39 - Prob. 60PCh. 39 - Prob. 61GPCh. 39 - Prob. 62GPCh. 39 - Prob. 63GPCh. 39 - Prob. 64GPCh. 39 - Prob. 65GPCh. 39 - Prob. 66GPCh. 39 - Prob. 67GPCh. 39 - Prob. 68GPCh. 39 - Prob. 69GPCh. 39 - Prob. 70GPCh. 39 - Prob. 71GPCh. 39 - Prob. 72GPCh. 39 - Prob. 73GPCh. 39 - Prob. 74GPCh. 39 - Prob. 75GPCh. 39 - Prob. 76GPCh. 39 - Prob. 77GP
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- If an atom has an election in the n = 5 state with m = 3, what are the possible values of l?arrow_forwardExplain how a hydrogen atom in the ground state (l = 0) can interact magnetically with an external magnetic field.arrow_forwardCheck Your Understanding Can the magnitude of Lzever be equal to L?arrow_forward
- Do the Balmer series and the Lyman series overlap? Why? Why not? (Hint: calculate the shortest Balmer line and the longest Lyman line.)arrow_forward(2) In this experiment, why couldn't we observe the series of spectral lines that arise from electrons falling to the ground state, nfinal = 1? This is the Lyman series, for which 22 (see eq. (16)) must be replaced by 12 in both the numerator and denominator of the equation: 2 =- 1 n2 n = R (n2-1)' 2,3,4,5, ..arrow_forward(6) (a) Show that the speed of an electron in the nth Bohr orbit of hydrogen is ac/n where a is the fine structure constant. (b) What would be the speed in a hydrogenlike atom with a nuclear charge of Ze?arrow_forward
- (a) Show that the speed of an electron in the nth Bohr orbit of hydrogen is ac/n, where a is the fine structure constant, equal to e/4neghc. (b) What would be the speed in a hydrogen like atom with a nuclear charge of Ze?arrow_forwardThe Lyman series comprises a set of spectral lines. All of these lines involve a hydrogen atom whose electron undergoes a change in energy level, either beginning at the n = 1 level (in the case of an absorption line) or ending there (an emission line). The inverse wavelengths for the Lyman series in hydrogen are given by 1 - where n = 2, 3, 4, ... and the Rydberg constant R, = 1.097 x 10' m-. (Round your answers to at least one decimal place. Enter your answers in nm.) %3D (a) Compute the wavelength for the first line in this series (the line corresponding to n = 2). nm (b) Compute the wavelength for the second line in this series (the line corresponding to n = 3). nm (c) Compute the wavelength for the third line in this series (the line corresponding to n = 4). nm (d) In which part of the electromagnetic spectrum do these three lines reside? O x-ray region O ultraviolet region O infrared region O gamma ray region O visible light regionarrow_forward(a) The Lyman series in hydrogen is the transition from energy levels n = 2, 3, 4, ... to the ground state n = 1. The energy levels are given by 13.60 eV En n- (i) What is the second longest wavelength in nm of the Lyman series? (ii) What is the series limit of the Lyman series? [1 eV = 1.602 x 1019 J, h = 6.626 × 10-34 J.s, c = 3 × 10° m.s] %3D Two emission lines have wavelengts A and + A2, respectively, where AA <<2. Show that the angular separation A0 in a grating spectrometer is given aproximately by (b) A0 = V(d/m)-2 where d is the grating constant and m is the order at which the lines are observed.arrow_forward
- (i) Using Bohr model for atomic hydrogen, obtain energy levels for the 2s, 3s and 3p states in the actual number with the unit of [eV]. We consider a transition that electron in the 3p state emits a photon and make a transition to the 2s state. What is the frequency v of this photon ? (ii) Now we do not include electron spin angular momentum, and just estimate an effect of a magnetic field B on this transition (Normal Zeeman effect) with orbital angular momentum. How many lines of optical transition do we expect ? What is the interval of the frequency in the field B = 0.1 Tesla ? (iii) In this situation, we do not expect transition from 3s to 2s state if the electron is initially in the 3s state, Explain the reason. (iv) We now consider an effect of magnetic field B to a free electron spin (not in Hydrogen, but a free electron). The magnetic field of B = 1.0 Tesla will split the energy level into two (Zeeman) levels. Obtain the level difference in the unit of [eV] from the value of…arrow_forward(II) Is the use of nonrelativistic formulas justified in the Bohr atom? To check, calculate the electron's velocity, v, in terms of c, for the ground state of hydrogen, and then calculate V1 - v²/c².arrow_forward(1) Based on Bohr model assumptions, prove that the wavelength equation of the hydrogen emitted 1 radiation is given by RH Answerarrow_forward
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